Conversions among different international temperature scales

Conversion among IPTS-68 and ITS-90

The International Temperature Scale of 1990 (ITS-90) was assembled to represent absolute thermodynamic temperature as good as possible. Conversion among the ITS-90 and the older IPTS-68 can be performed by two polynomials for different temperature ranges.

Equation

The Blue Book (Preston-Thomas & Quinn 1997) gives a polynomial to reproduce (t90-t68) differences in the range of -200°C to 630°C, with an uncertainty of 1.5mK below and 1mK above 0°C:

Between 630.615°C and 1064.18°C Rusby et al. (1994) introduced a revised polynomial for calculating (t90-t68). It replaces the original equation given by the first edition of the Blue Book (Preston-Thomas 1990). In the 1997 edition of the Blue-Book these changes are listed in the Amendment section (Preston-Thomas & Quinn 1997, Page v):

Coefficients are given in the table below. Although the given equations define conversion from ITS-90 to IPTS-68 they can be used in both directions. When using this equation for an IPTS-68 to ITS-90 conversion the deviation from an (t90-t68) conversion is <=0.05mK within the range -200°C < t < 630°C and <=0.26mK within 630.615°C < t < 1064.18°C (personal communication J. Fischer and S. Friederici, Physikalisch Technische Bundesanstalt, www.ptb.de).

Table for the coefficients for calculating the difference (t90-t68)

-200°C to 630°C

630.615°C to 1064.18°C

a0=0

b0=+7.8687209*101

a1=-0.148759

b1=-4.7135991*10-1

a2=-0.267408

b2=+1.0954715*10-3

a3=+1.080760

b3=-1.2357884*10-6

a4=+1.269056

b4=+6.7736583*10-10

a5=-4.089591

b5=-1.4458081*10-13

a6=-1.871251

a7=+7.438081

a8=-3.536296

Algorithm

For a given temperature in aTemp the function returns the difference between ITS-90 and IPTS-68 in DeltaT. The return value of the function is TRUE, iff the passed value in aTemp is within -200°C to 1064.18°C. Between 630.00°C and 630.15°C none of the functions is officially valid, but both reasonable. Investigating polynomials it is found that they intersect at approximately 630.147°C. For practical reasons it is useful to switch between polynomials at this point. Within the range 630.00°C to 630.15°C deviations from officially tabulated values are <0.7mK (personal communication J. Fischer and S. Friederici, Physikalisch Technische Bundesanstalt, www.ptb.de).

// check whether aTemp is in a valid range If (aTemp >= -200) And (aTemp <= 1064.18) THen Begin If aTemp <= 630.147 then Begin // if temp is below or equal 630.147°C use first polynomial TempFrac := aTemp/630;

Simple conversion between IPTS-48 and IPTS-68 in the range -2°C to 30°C

Within the range of -2°C to 30°C a simple conversion between IPTS-48 and IPTS-68 can be used. This conversion is supported by the Joint Panel on Oceanographic Tables and Standards (JPOTS) for oceanographic issues (ICES documentation on http://www.ices.dk/ocean/procedures/its.htm, updated 31.January 2005).

Equation

The formula was constructed by Fofonoff and published in Fofonoff & Bryden (1975):

References

Simple conversion between IPTS-68 and ITS-90 in the range -2°C to +40°C

For biological and oceanographic purposes, as well as for a couple of other applications the temperature range between -2°C and 40°C is most important. In this range IPTS-68 and ITS-90 scales are nearly linear and show a similar slope. Thus, a more simple conversion may be used. This conversion was recommended by Saunders (1990) and is supported by the Joint Panel on Oceanographic Tables and Standards (JPOTS) (ICES documentation on http://www.ices.dk/ocean/procedures/its.htm, updated 31.January 2005).

Equation

t68 = t90 * 1.00024

t90 = t68 * 0.99976

Approximation with these formulas result in deviations <0.5mK from officially tabulated values between -2°C to 40°C (personal communication J. Fischer and S. Friederici, Physikalisch Technische Bundesanstalt, www.ptb.de) compared to the conversion given by Preston-Thomas & Quinn (1997).

Algorithm

The conversion can be simply implemented in the code whenever needed. Thus, no individual functions are given.